Global existence of a strong solution to the initial value problem for the Nernst-Planck-Navier-Stokes system in high space dimensions

Xiangsheng Xu

Global existence of a strong solution to the initial value problem for the Nernst-Planck-Navier-Stokes system in high space dimensions

Analysis of PDEs 2026-01-13 v5

Authors: Xiangsheng Xu

Abstract

We study the existence of a strong solution to the initial value problem for the Nernst-Planck-Navier-Stokes (NPNS) system in $\mathbb{R}^N, N\geq 3$ . The system describes the electrodiffusion of ions in a viscous Newtonian fluid. A strong solution is obtained in any dimension of space without constraints on the number of species or the size of the given data.

Keywords

Nernst-Planck-Navier-Stokes system strong solution global existence initial value problem high dimensions electrodiffusion

Cite

@article{arxiv.2404.16433,
  title  = {Global existence of a strong solution to the initial value problem for the Nernst-Planck-Navier-Stokes system in high space dimensions},
  author = {Xiangsheng Xu},
  journal= {arXiv preprint arXiv:2404.16433},
  year   = {2026}
}

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